Question

Calculate the wavelength of a nitrogen molecule moving at a speed of 523m/s.

Answer 1

The de-Broglie wavelength of the nitrogen molecule is 0.0272 nm

Step-by-step explanation:

The mass, m, of the nitrogen molecule, N₂ = 14.0076u = 28.0152 × 1.66 × 10⁻²⁷ kg

`v_(rms)` of N₂ = 523 m/s

The de-Broglie wavelength is given as follows;

`de-Broglie \, wavelength = (h)/(m* v_(rms))`

Where:

h = Planck's constant = 6.62607004 × 10⁻³⁴ m²·kg/s

Plugging in the values, we have;

`de-Broglie \, wavelength = (6.62607004 * 10^(-34))/(28.0152 * 1.66 * 10^(-27)* 523) = 2.72* 10^(-11) \, m`

Hence, the de-Broglie wavelength of the nitrogen molecule = 0.0272 nm.